1) Field of the Invention
The present invention relates to an optical scanning device and an image forming apparatus, and in particular, to a lens that is used in an optical system for the optical scanning device.
2) Description of the Related Art
In recent years, in image forming apparatuses like a digital copying machine and a laser printer, density of image formation by optical scanning has been increasing. As a result, there is an increasing demand for producing a smaller light spot to form optical images on a photosensitive member. Characteristic of a lens have a great influence on the diameter of a light spot produced by the lens. In case of the glass lenses, shapes into which the glass lens can be machined are limited; moreover, it is very difficult to accurately hold the glass lens during machining. On the other hand, lenses that are made of resin have no such problems, and are cheaper than the glass lenses.
However, surface curvatures, thicknesses, and refractive indices of the resin lenses vary greatly with temperature. When the surface curvatures, thicknesses, and refractive indices vary, focus positions of the resin lens change, spot diameters increase, and this results into a degraded image. Moreover, wavelength of a semiconductor laser serving as a light source also changes with the surrounding temperature. Since the lens made of resin has large dispersion power compared with the glass lens, again, a focus position fluctuates and a spot diameter increases to cause deterioration in an image.
FIGS. 7A and 7B are diagrams of an example of a conventional scanning optical system 100. All the lenses used in the conventional scanning optical system 100 are made of resin; moreover, a diffractive optical surface is not used. FIG. 7A is a plan view of the optical system viewed from above and FIG. 7B is a schematic diagram in which the lenses are arranged on a straight line to represent distances among respective lens surfaces. This scanning optical system 100 includes a light source 11, such as by a semiconductor laser, a coupling lens 12, an aperture 13, an anamorphic lens 14, a polygon mirror 15, a deflector side scanning lens 16, an image surface side scanning lens 17, a dust-proof glass 18, and an image surface 19. Light beams emitted from the light source 11 are changed to weakly diverging rays by the coupling lens 12, pass through the aperture 13, and are changed into parallel beams in a main scanning direction and light beams, which focus near the polygon mirror 15, in a sub-scanning direction by the anamorphic lens 14 forming a first optical system. Further, the light beams are deflected by the polygon mirror 15 and focused on an image surface through the dust-proof glass 18 by the deflector side scanning lens 16 and the image surface side scanning lens 17. The light source 11 and the coupling lens 12 are fixed to an identical member made of aluminum.
Optical system data are indicated below. A light source wavelength is set to 780.1 nanometers at 25° C. and 786.5 nanometers at 45° C.
A light source side surface shape of the coupling lens 12 is a coaxial aspheric surface represented as follows:x=(h^2/R)/[1+√{1−(1+K)(h/R)^2}]+A4·h^4+A6·h^6+A8·h^8+A10·h^10  (1)
In the equation (1), h is a distance from an optical axis, R is a paraxial curvature radius, K is a cone constant, A4, A6, A8, and A10 are high-order coefficients, and x is a depth in an optical axis direction.
The coefficients are set as follows:
R=86.09118
K=361.987634
A4=−0.827025E−04
A6=−0.413360E−05
A8=0.942600E−06
A10=−0.936986E−07
An image surface side surface shape of the coupling lens 2 is an aspheric surface represented by the equation (1), and the coefficients are set as follows:
R=−8.71000
K=−0.310240
A4=0.592273E−04
A6=0.250465E−06
A8=0.119847E−06
A10=−0.563217E−08
Data for the anamorphic lens 14 are as follows:
A light source side surface shape of this anamorphic lens 14 is an anamorphic surface represented as follows:x={(1/Rm)·y^2+(1/Rs)·z^2}/[1+√{1−(y/Rm)^2−(z/Rs)^2}]  (2)
In the equation (2), y is a main scanning direction distance from the optical axis, z is a sub-scanning direction distance from the optical axis, Rm is a main scanning direction curvature radius, Rs is a sub-scanning direction curvature radius, and x is a depth in the optical axis direction.
The coefficients are set as follows:
Rm=500
Rs=35.83
An image surface side surface shape of the anamorphic lens 14 is a plane.
A light source side surface shape of the deflector side scanning lens 16 is a coaxial aspheric surface represented by the equation (1).
The coefficients are set as follows:
R=−312.6
K=2.667
A4=1.79E−07
A6=−1.08E−12
A8=−3.18E−14
A10=3.74E−18
An image surface side surface shape of the deflector side scanning lens 16 is a coaxial aspheric surface represented by the equation (1).
The coefficients are set as follows:
R=−83.0
K=0.02
A4=2.50E−07
A6=9.61E−12
A8=4.54E−15
A10=−3.03E−18
Vertexes of both the surfaces deviate upward by 1.16 millimeters with respect to a main beam in FIG. 7.
A light source side surface shape of the image surface side scanning lens 17 is a non-arc represented by equation (3) in the main scanning direction. A sub-scanning curvature radius changes continuously as represented by equation (4) in the sub-scanning direction.x=(y^2/Rm)/[1+√{1−(1+K)(y/Rm)^2}]+A4·y^4+A6·y^6+A8·y^8+A10·y^10  (3)
In the equation (3), y is a main scanning direction distance from the optical axis, Rm is a main scanning paraxial curvature radius, K is a cone constant, A4, A6, A8, and A10 are high-order coefficients, and x is a depth in the optical axis direction.Rs(y)=Rs+Σbj·y^j (where j=1, 2, 3, . . . )  (4)
In the equation (4), y a main scanning direction distance from the optical axis, Rs(y) is a sub-scanning radius in the main scanning direction distance y from the optical axis, Rs is a sub-scanning radius on the optical axis, and bj (where j=1, 2, 3, . . . ) are high-order coefficients.
The coefficients are set as follows:
Rm=−500
K=−71.73
A4=4.33E−08
A6=−5.97E−13
A8=−1.28E−16
A10=5.73E−21
Rs=−47.7
b2=1.60E−03
b4=−2.32E−07
b6=1.60E−11
b8=−5.61E−16
b10=2.18E−20
b12=−1.25E−24
An image surface side surface shape of the image surface side scanning lens 17 is a toroidal surface, and a sub-scanning shape is an arc represented by equation (5) and is a shape rotated around an axis parallel to the sub-scanning direction Rm apart in the optical axis direction from a vertex of this arc.x=(z^2/Rs)/[1+√{1−(z/Rs)^2}]  (5)
In the equation (5), y is a main scanning direction distance from the optical axis, Rs is a sub-scanning paraxial curvature radius, and x is a depth in the optical axis direction.
The coefficients are set as follows:
Rm=−1000
Rs=−23.38
Vertexes of both the surfaces deviate upward by 1.21 millimeters with respect to the main beam in FIG. 7.
Surface intervals are set as follows (unit: millimeters).
d1=12.741
d2=3.8
d3=102.8
d4=3.0
d5=69.3
d6=51.7
d7=31.4
d8=78.0
d9=3.5
d10=143.62
In this optical system, a dust-proof glass 8 with a thickness of 1.9 millimeters (at 25° C.) is inserted to perform the above calculations. A refractive index of this glass is set to 1.511161 at a beam wavelength of 780.1 nanometers and a temperature of 25° C. and 1.511161 at a beam wavelength of 786.5 nanometers and a temperature of 45° C. and a linear expansion coefficient of the glass is set to 7.5E−06K−1.
All the lenses are made from the same resin material. Moreover, refractive indices of the lenses are 1.523946 at a beam wavelength of 780.1 nanometers and a temperature of 25° C., and 1.522105 at a beam wavelength of 786.5 nanometers and a temperature of 45° C., and a linear expansion coefficient of the lenses is 7.0E−05K−1.
When a focus position with respect to an image surface position is calculated taking into account changes in a beam wavelength, a refractive index, a surface shape, and a thickness according to a temperature under the conditions described above, a result shown in FIG. 8 is obtained. It is seen from this result that, when the environmental temperature changes from 25° C. to 45° C., the focus position deviates in the main scanning direction from 0.0 millimeters to 11.6 millimeters and in the sub-scanning direction from 0.0 millimeters to 3.3 millimeters.
As means for solving this problem, for example, Japanese Patent Application Laid-Open No. 2002-214556 discloses a method of correcting the change in a focus position by combining at least three lenses in an optical system before a deflector (polygon mirror). In addition, Japanese Patent Application Laid-Open No. H10-333070 discloses a method of correcting the change in a focus position by providing a diffractive optical surface in a scanning lens.
However, in the conventional technology disclosed in Japanese Patent Application Laid-Open No. 2002-214556, cost increases due to an increase in the number of lenses and, even in this case, at least one glass lens is required, which further increases cost.
The conventional technology disclosed in Japanese Patent Application Laid-Open No. H10-333070 has a problem in that, since a scanning lens used in the conventional technology has a wide area through which light beams pass, it takes time to machine a diffractive surface, which leads to an increase in cost.